Talk:MARS voting: Difference between revisions
→Tie handling
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::It feels like there's a step missing, though. Something like, if there's a cycle or tie, look at the score and drop the lowest candidate and iterate, like IRV. In the MARS algorithm, there is no candidate elimination step, so where would that go? --[[User:Ŝan|Ŝan]] ([[User talk:Ŝan|talk]]) 22:15, 24 February 2021 (UTC)
:::In the above example (ABC cycle, AB tie by score) the process is as follows: Sum up all unmodified scores and find the score winner. There are two score winners tied so we pick either of them (just ignore how for a moment). We pick A and then compare the other candidates to A. We find that C>A and then compare the candidates against C, find that B>C, again compare against B and find that A>B. So we discovered a cycle. In case of a cycle we pick the score winner, but here again A and B are tied. We ignore C because they are not the score winner. Just comparing A and B it is clear that B should win by preference over A.
:::So there two groups of ties which can be solved by preference and one which can not be solved:
:::* Tied in a match against another candidate, or score in the first round. These are essentially the same.
:::* Tied by score in the case we found a cycle.
:::* True tie by score and preference.
:::Ties, except true ties, can be resolved by preference. So the the rule for ties just has to be "When there is any tie, pick the majority winner if possible." Unless I missed something. To restate your above list:
:::# The winner ''of a round'' is the one with the highest modified score (HMS, score+modifier, ''in the first round the modifier is 0 for all candidates''); or
:::# If there's an HMS tie, then the winner is the leading ''tied'' candidate with the highest cardinality (number of votes); or
:::# If there's a cardinality tie, then the election is a hard tie with no possible winner.
:::For cycles:
:::# If there's a cycle, then the ''final'' winner is the leading candidate with the highest unmodified score (HUS); or
:::# If there's an HUS tie ''within the cycle'', then the winner is the leading ''tied'' candidate with the highest cardinality (number of votes).
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